câu 1 : giả sử chữa số cần tìm là \(\overline{abc}\)
ta có : \(\overline{abc}⋮45\Rightarrow c\in\left\{0;5\right\}\) \(\Rightarrow\left[{}\begin{matrix}\overline{abc}=\overline{a\dfrac{a}{2}0}\\\overline{abc}=\overline{a\dfrac{a+5}{2}0}\end{matrix}\right.\)
ta lại có : \(\overline{abc}⋮45⋮9\) \(\Rightarrow a+b+c⋮9\)
th1: \(\overline{abc}=\overline{a\dfrac{a}{2}0}\) \(\Rightarrow a+\dfrac{a}{2}\in\left\{0;9;18...\right\}\)
\(\Rightarrow a\in\left\{0;6;12...\right\}\) \(\Rightarrow a=6\)
\(\Rightarrow\overline{abc}=630\)
th1: \(\overline{abc}=\overline{a\dfrac{a+5}{2}5}\) \(\Rightarrow a+\dfrac{a+5}{2}+5\in\left\{0;9;18...\right\}\)
\(\Rightarrow a\in\left\{-5;1;7;13\right\}\) \(\Rightarrow a=1;a=7\)
\(\Rightarrow\overline{abc}=135;\overline{abc}=765\)
vậy số cần tìm là \(630;135;765\)
câu 2 : ta có : \(A=2^1+2^2+2^3+...+2^{30}\)
\(\Leftrightarrow A=2\left(1+2+2^2+2^3+2^4+2^5\right)+...+2^{25}\left(1+2+2^2+2^3+2^4+2^5\right)\)
\(=2\left(63\right)+...+2^{25}\left(63\right)=63\left(2+...+2^{25}\right)\)
\(=7.9\left(2+...+2^{25}\right)⋮9\)
vậy \(A\) chia hết cho \(9\)